Clifford Algebras , Clifford Groups , and a Generalization of the Quaternions : The Pin and Spin Groups

@inproceedings{Gallier2001CliffordA,
  title={Clifford Algebras , Clifford Groups , and a Generalization of the Quaternions : The Pin and Spin Groups},
  author={Jean H. Gallier},
  year={2001}
}
One of the main goals of these notes is to explain how rotations in R are induced by the action of a certain group Spin(n) on R, in a way that generalizes the action of the unit complex numbers U(1) on R, and the action of the unit quaternions SU(2) on R (i.e., the action is defined in terms of multiplication in a larger algebra containing both the group Spin(n) and R). The group Spin(n), called a spinor group, is defined as a certain subgroup of units of an algebra Cln, the Clifford algebra… CONTINUE READING

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